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A087977 a(n) is the first term in the first chain of at least n consecutive numbers each having exactly four distinct prime factors. 6
210, 7314, 37960, 134043, 357642, 1217250, 1217250, 14273478, 44939642, 76067298, 163459742, 547163235, 2081479430, 2771263512, 11715712410, 17911205580, 56608713884, 118968284928, 118968284928, 585927201062 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Eggleton and MacDougall show that there are no more than 419 terms in this sequence. - T. D. Noe, Oct 13 2008

a(24) > 10^13. - Donovan Johnson, Jan 15 2009

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..23

Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235-248.

EXAMPLE

a(6) = a(7) = 1217250 because the relevant 7 successive numbers have 4 distinct prime factors:

  1217250 = 2   *  3^2 *   5^3 * 541;

  1217251 = 7   * 17   *  53   * 193;

  1217252 = 2^2 * 23   * 101   * 131;

  1217253 = 3   * 47   *  89   *  97;

  1217254 = 2   * 19   * 103   * 311;

  1217255 = 5   * 13   *  61   * 307;

  1217256 = 2^3 *  3   *  67   * 757.

MATHEMATICA

k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={4}, k++ ]; Print[k], {n, 1, 8}]

Module[{d4=Table[If[PrimeNu[n]==4, 1, 0], {n, 143*10^5}]}, Flatten[Table[ SequencePosition[d4, PadRight[{}, n, 1], 1], {n, 8}], 1][[All, 1]]] (* Requires Mathematica version 10 or later *) (* This generates the first 8 terms of the sequence *) (* Harvey P. Dale, Aug 25 2017 *)

CROSSREFS

Cf. A080569 (m=3), A064708 (m=2).

Cf. A087978, A138206, A138207, A154573.

Sequence in context: A103604 A257711 A061133 * A185042 A023905 A035840

Adjacent sequences:  A087974 A087975 A087976 * A087978 A087979 A087980

KEYWORD

nonn,fini

AUTHOR

Labos Elemer, Sep 26 2003

EXTENSIONS

More terms from Don Reble, Sep 29 2003

a(13)-a(19) from Donovan Johnson, Mar 06 2008

a(20)-a(23) from Donovan Johnson, Jan 15 2009

STATUS

approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)